Problem: In $\triangle PQR,$ the sum of $\angle P$ and $\angle Q$ is $60^\circ.$ What is the measure of $\angle R?$
Solution: The sum of the three angles in any triangle is always $180^\circ.$ In $\triangle PQR,$ the sum of $\angle P$ and $\angle Q$ is $60^\circ,$ and thus $\angle R$ must measure $$180^\circ - 60^\circ = \boxed{120^\circ}.$$